Permutations corresponding rigid motions of a rectangle/rhombus.

In summary, the task is to find the permutations of vertices that represent the rigid motions of a rectangle and a rhombus (both not being squares). This involves considering rotations and flips, and possibly dealing with angles.
  • #1
kathrynag
598
0

Homework Statement


Find the permutations that correspond to the rigid motions of a rectangle that is not a square. Do the same for the rigid motions of a rhombus that is not a square.


Homework Equations





The Attempt at a Solution


I began by drawing the rectangle and rhombus and labeling sides. I know I need to do something with permutations of the vertices. I feel like I need to do something with angles since they are not right angles, but I can not figure out what to do with angles.
 
Physics news on Phys.org
  • #2
Do I deal with angles at all? I know I need to do something with rotations and flips.
 

What is a permutation?

A permutation is a way of arranging a set of objects in a specific order. In the context of rigid motions of a rectangle or rhombus, a permutation represents the different ways in which the shape can be rotated, reflected, or translated.

How many permutations are there for a rectangle/rhombus?

For a rectangle, there are 8 possible permutations: 4 rotations (0°, 90°, 180°, and 270°) and 4 reflections (horizontal, vertical, and the two diagonal lines). For a rhombus, there are 4 possible permutations: 2 rotations (0° and 180°) and 2 reflections (horizontal and vertical).

What is a rigid motion?

A rigid motion is a transformation that preserves the size and shape of an object. In the context of a rectangle or rhombus, a rigid motion can be a rotation, reflection, or translation.

How can permutations be used in real life?

Permutations can be used in real life to represent different arrangements of objects or people. For example, the seating arrangements at a dinner party or the order of a playlist on a music app can be thought of as permutations.

Is there a formula for calculating the number of permutations?

Yes, the formula for calculating the number of permutations is n!, where n is the number of objects being arranged. In the case of a rectangle with 4 sides, n = 4, so the number of permutations would be 4! = 24.

Similar threads

Integrating a Rhombus: Solving for Area Using the Change of Variables Formula
    • Calculus and Beyond Homework Help
Replies
8
Views
1K
Showing that dihedral 4 is isomorphic to subgroup of permutations
    • Calculus and Beyond Homework Help
Replies
3
Views
3K
Showing that a subgroup of Sym(4) is isomorphic to D_8
    • Calculus and Beyond Homework Help
Replies
1
Views
929
Multiplying permutation cycles
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Two Conjectures about Permutations in ##S_n##
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Proving Graph Theory with Group Permutations | G = Sn and S Set
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
How Do You Solve the Rhombus Side Length in Rectangle ABCD?
    • Calculus and Beyond Homework Help
Replies
2
Views
3K
Hyperbolic Geometry (Rectangles)
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Permutations of (abc)(efg)(h) in S7
    • Calculus and Beyond Homework Help
Replies
7
Views
2K
Proof using Permutation Symbols
    • Calculus and Beyond Homework Help
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top